Epidemiology generates a major part of the scientific knowledge needed for programs in cancer prevention and regulation of carcinogenic exposures. Case-control and cohort studies serve not only to identify carcinogenic risk factors but also to investigate dose-time-response relationships for purposes of quantitative risk assessment and the planning of intervention strategies. Statistical concepts are crucial for understanding the logical foundations of such studies and for devising appropriate methods of study design and data analysis. The broad objective of this proposal is to create new and efficient statistical methods of design and analysis of epidemiolgica studies that are suitable for immediate application by medical epidemiologists and others without extensive technical background. We plan to continue work on 'two stage' designs that are particularly valuable for retrospective cohort studies, where data on disease and primary exposure already exist for large numbers, but where the covariable data needed to adjust confounding require costly interviews or laboratory analyses that can only be carried out for a smaller sample. We plan to extend earlier work on nonparametric estimation of relative risk functions that takes advantage of the enormous progress in computer technology and the emerging statistical theory of semiparametric models. Robust and efficient estimates of fixed effects and variance components in random and mixed generalized models will be investigated for use with problems of overdispersion and with correlated data from longitudinal or repeated measures studies. Empirical Bayes methods for longitudinal studies that correctly account for uncertainty about the variance components, likelihood methods for the estimation of relative risks associated with disease susceptibility genes in family studies and small sample methods for robust statistical inference in logistic regression models also will be developed. Newly developed methods will be tested immediately on several sets of data of importance in cancer epidemiology in order to ascertain their practical utility. Sampling characteristics will be investigated by computer simulation using parameter settings suggested by real applications. The new methods will be implemented on microcomputers and described in review articles and short courses so as to facilitate their transmission to research workers.